Question

Calculate the correlation coefficient for the following data.

$\begin{array}{cc}X& Y\\ 2& 4\\ 3& 6\\ 4& 9\\ 5& 10\\ 6& 11\\ 7& 13\\ 8& 17\end{array}$

• A. 0.878
• B. 0.925
• C. 0.965
• D. 0.982

Answer 1

The correct option is D

0.982

$\begin{array}{cccccccc}x& y& x-\overline{x}& (x-\overline{x}{)}^2& (y-\overline{y})& (y-\overline{y}{)}^2& (x-\overline{x})(y-\overline{y})& \\ 2& 4& -3& 9& -6& 36& 18& \\ 3& 6& -2& 4& -4& 16& 8& \\ 4& 9& -1& 1& -1& 1& 1& \\ 5& 10& 0& 0& 0& 0& 0& \\ 6& 11& 1& 1& 1& 1& 1& \\ 7& 13& 2& 4& 3& 9& 6& \\ 8& 17& 3& 9& 7& 49& 21& \\ & & & \sum =28& & \sum =112& \sum =55& \end{array}$

$\overline{x}=\frac{\sum x}{n}=\frac{35}{7}=5$
$\overline{y}=\frac{\sum y}{n}=\frac{70}{7}=10$

$r=\frac{{\sum }_{i=1}^n(x_i-\overline{x})(y_i-\overline{y})}{\sqrt{{\sum }_{i=1}^n(x_i-\overline{x}{)}^2}\sqrt{{\sum }_{i=1}^n(y_i-\overline{y}{)}^2}}=\frac{55}{\sqrt{28\times 112}}=\frac{55}{56}=0.982$